where \(k\)  runs over all intact fibers. Such \(\gamma \) -dependent stress redistribution has been explored earlier [1]}, [2]} in the context of fiber bundle model. With the present rule, a high \(\gamma \)  stands for a low stress release range and hence closer to LLS scheme. On the other hand, for low \(\gamma \) , the model enters the GLS or mean-field limit. Earlier studies pointed out a critical \(\gamma _c\)  for both 1d [2]} and 2d [1]} fiber bundle model around which this transition from LLS to GLS limit takes place. After such redistribution, other fibers can break due to the elevated local stress profile and the stress is again redistributed. This starts an avalanche at the same external stress. The size \(s\)  of an avalanche is the number of fibers broken during the process. The energy emitted during an avalanche of size \(s\)  is represented as follows:
\(E(s) = \displaystyle \sum _{1}^s \displaystyle \frac{1}{2}h_i^2\) 
